# Questions tagged [bivariate-distributions]

For questions on bivariate distributions, the combined probability distribution of two randomly different variables.

144 questions
1answer
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### Conditional distribution for two random variables

I recently came across and exercise from a past exam and I was wondering how to solve it. Two independent random variables $A$ and $B$ are given and they both follow the exponential distribution but ...
0answers
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2answers
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### calculate $\operatorname{cov}(X,Y)$ from $f_{x,y}(x,y)$

I have the following density function: $$f_{x, y}(x, y) = \begin{cases}2 & 0\leq x\leq y \leq 1\\ 0 & \text{otherwise}\end{cases}$$ We know that $\operatorname{cov}(X,Y) = E[(Y - EY)(X - EX)]$...
1answer
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### Calculate probability $P(X_1\geq1/2, X_2\geq1/2)$ for $F_{X_1,X_2}$

I am studying for an exam and came across this example to calculate probability $P(X_1\geq1/2, X_2\geq1/2)$ for $F_{X_1,X_2}$ = $1/2x_1x_2(x_2^2+x_1^2)$ if $0\leq x_1\leq 1,0\leq x_2\leq 1$. The ...
1answer
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0answers
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### Is the joint distribution of any two uncorrelated normally distributed random variables bivariate normal?

Originally I was only going to ask if the joint distribution of any two normally distributed is random variables bivariate normal, however it seems that a large set of counterexamples can be found ...
1answer
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1answer
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### Finding the conditional probability given the joint probability density function

f(x,y) = e^-x if 0 <= y <=x < \infty i need to find the P(X<3|Y<2) & P(X<3|Y=2). i'm struggling with the first probability. i'm not sure how to evaluate the conditional given ...